Topology optimization of bi-modulus material structures involving geometric nonlinearity

Many materials in practical engineering have bi-modulus characteristics, such as concrete, rubber, ceramic materials, etc. However, existing topology optimization techniques are generally based on the assumption of single modulus material, which leads to design results deviating from actual situations and even catastrophic damage. This paper proposes a topology optimization method for bi-modulus material structures considering geometric nonlinearity. Firstly, an innovative bi-modulus material smooth constitutive model based on the hyperbolic tangent function in strain space was constructed, which can effectively achieve finite element analysis of bi-modulus material structures; Subsequently, an efficient iterative solution technique for bi-modulus material structures coupling geometric nonlinearity and material nonlinearity was proposed; Then, a topological optimization model was constructed to minimize the static compliance of bi-modulus material structures under geometric nonlinearity conditions, and sensitivity analysis of the objective function to design variables was carried out; Finally, the effectiveness of the proposed method was verified through a series of numerical examples, and the influence of design parameters on the design results was studied. This paper presents an efficient design technique for bi-modulus material structures considering geometric nonlinearity, which has important theoretical and engineering practical value for achieving efficient design of bi-modulus material structures.